DTIC ADA542036: Sediment Acoustics: Wideband Model, Reflection Loss and Ambient Noise Inversion

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Sediment acoustics: Wideband model, reflection loss and ambient noise inversion

Nicholas P. Chotiros
Applied Research Laboratories
The University of Texas at Austin, TX 78713-8029
phone: [phone] fax: [phone] email: [email protected]

Award Number: N00014-06-1-0125
http://www.arlut.utexas.edu/

LONG-TERM GOALS

Physically sound models of acoustic interaction with the ocean floor including penetration, reflection
and scattering in support of MCM and ASW needs.

OBJECTIVES

(1) Consolidation of the BIC08 model of sediment acoustics, its verification in a variety of sediment
types, parameter reduction and documentation in preparation for transition. (2) A new model of
sediment reflection based on a mixture of models suitable for shallow water sonars. (3) Coupling of
BIC08 to rough surface scattering models.

APPROACH

(1) Consolidation of the BIC08 model: This model contains plausible physical processes. It is based on
the Biot-Stoll grain contact squirt flow and shear viscous drag (BICSQS) model, which includes squirt
flow at the grain-grain contacts [Chotiros, Isakson 2004], combined with improvements in squirt flow
modeling, the frame virtual mass extension t o account for t he random grains rotation [ Chotiros,
Isakson 2007], and the high-frequency viscous drag correction [Chotiros, Isakson 2008]. The approach
is to reconcile common parameters in the different components, and consolidate the input parameters to
reduce the p arameter co unt. Further t ests ar e p lanned t o co ntinue t o t est i t against ex perimental
measurements and extend it to a w ider variety of ocean sediments, through participation in future
shallow-water and sediment acoustics experiments. New experimentation methods are envisioned,
including the exploitation of ambient noise for bottom characterization using a compact, partially
buried array.

(2) A new model of sediment reflection: This is a new approach to modeling ocean sediments that
recognizes that the sediment is often patchy. The reflection measurements from the SAX04 experiment
[Isakson, Chotiros, Camin, Piper 2010] are an extreme example. This suggests a n ew approach to
modeling bot tom r eflection a s a r andom pr ocess, i n w hich e ach bottom bounce contains bot h a
deterministic as well as a random component. This is consistent with recent findings that bottom
backscatter is often well described by a mixture of processes [Lyons and Abraham 1999]. It will lead
to more realistic bottom models for sonar performance prediction.
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Sediment acoustics: Wideband model, reflection loss and ambient noise
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(3) Coupling of BIC08 to rough surface scattering models: Since the real ocean bottom is rough, it is
necessary to be able to combine the BIC08 model with a rough interface, in order to obtain a realistic
model of the bottom. For a computationally fast solution, a ray-based approach is likely to be a
practical solution, but for accuracy, a finite element approach would be best. This task also includes
experimental support equipment to measure seafloor roughness, to allow rough interface scattering
models to be tested with at-sea experimental measurements.

WORK COMPLETED

Following the three tasks mentioned in the approach, the work completed may be divided into three
corresponding sections:

(1) Consolidation of the new BIC08 model: There are at least two issues to resolve in order to move
forward. One is an accurate expression of shear wave speed in a granular medium. Another is the
reconciliation of parameter values that are used in different components of the model.

Regarding the expression for shear wave speed, it was shown that the shear wave speed in a granular
medium is less than that in an elastic solid of the same shear modulus-to-density ratio. Shear and
compressional wave speeds were derived for granular media using a conservation of energy
approach. The grains were assumed to be spherical with elastic Hertzian contacts of constant stiffness.
The affine approximation was used to determine the relative displacement of grain centers, and it was
also assumed that the grains are small compared to a wavelength, consistent with the effective medium
approximation. Potential and kinetic energies associated with linear motion were the same as those
in an elastic solid, but it was found that shear wave propagation in a granular medium involves
additional energies associated with grain rotation. The partition of energies results in a reduction in the
shear wave speed, relative to an elastic solid of the same shear modulus-to-density ratio. It was shown
that the reduction is an inherent property of granular media, independent of any departure from the
affine approximation or fluctuations in coordination number or contact stiffness. The predicted wave
speed ratios are consistent with published measurements [Chotiros and Isakson 2010].

Regarding the reconciliation of parameter values, the effort is concentrated about the physics of the
fluid film at the grain to grain contact. This fluid film is likely to be very thin, and consequently it may
involve new physics related to thin film viscosity. It has been recently found that, for nanometer-scale
interfacial separations, the effective viscosity is many orders of magnitude greater than that of bulk
water [Goertz, Houston, and Zhu 2007]. Future work will explore the relevance of the new physics of
thin film viscosity.

(2) A new model of sediment reflection: The reflection measurements from the SAX04 experiment
[Isakson, Chotiros, Camin, Piper 2010] show that the sediment can be highly inhomogeneous.
Through-the-sensor measurements of bottom backscattering strength, using the AN/SQS-53C sonar
and the SABLE system, as well as similar measurements through the AN/SQQ-32 sonar, have also
shown similar patchiness on larger scales. The heterogeneity is on a scale that is likely to be too fine to
be properly mapped and may change as a function of time, and therefore it has to be treated
statistically. In this approach, the key parameters are the amplitude and the spatial correlation function
of the fluctuations.

(3) Coupling of BIC08 to rough surface scattering models: There are some practical issues to be
resolved, regarding the spatial sampling of the medium for finite element modeling. In sandy
sediments, the Biot slow wave and the shear wave, which are predicted to have low wave speeds,
require very dense meshing of the medium model. A similar problem exists with elastic media with
low shear wave speeds. A method to reduce the mesh density is needed before work can continue. It
was decided that the work should start with the simpler problem, i.e. the elastic medium with a low
shear wave speed. Since a low shear wave speed is usually accompanied by high attenuation, the
approach is to model the medium as a fluid surrounded by a thin elastic layer. The thin elastic layer
will provide the proper reflection and transmission coefficient and should be thick enough that the
shear wave would be completely absorbed before it reaches the fluid core. The compressional wave
would pass from the elastic layer into the fluid core with minimal reflection since the impedances are
perfectly matched. Similarly, when a wave is transmitted from the fluid core into the elastic layer, there
should be minimal shear wave conversion. At the outer boundary, the composite would behave
indistinguishably from an elastic solid with a slow shear wave. Tests made with OASES showed that
the approach may be feasible.

RESULTS

The results are presented in the same order as the work completed:

(1) Consolidation of the new BIC08 model has made some progress: A key issue is an accurate
expression for shear wave speed in a granular medium. The grain motion for shear and compressional
waves is illustrated in Fig. 1 (a) and (b), respectively. In both cases, a half cycle including a peak, a null
and a trough are shown. At the peak and trough of the shear wave, the grains are displaced from their
equilibrium positions. At the null, midway between the peak and trough, the linear velocity, and hence
kinetic energy, is at a maximum. In addition, there is a grain rotation, which reaches a maximum at the
null. The combination of shear strain and grain rotation produces conflicting shear stresses at the grain-
grain contacts and a significant amount of potential energy. The particle motion of a compressional
wave is relatively straightforward. There is no average grain rotation. At the maximum linear
displacement, the potential energy is also maximum. At the null, the linear particle velocity amplitude
and kinetic energy are at maximum, and the grains are compressed.

Fig. 1. Illustration of (a) shear and (b) compressional wave motion, particle displacements and
rotations at the peaks, zeros, and troughs, in a granular medium with Hertzian contacts.
[There are two panels. The top panel illustrates grain motion in response to the passage of a shear
wave from left to right. The unperturbed particle positions are shown in the background. It shows
shear strain at the extremities of vertical motion, and grain rotation at the null. The bottom panel
shows grain motion in the presence of a compressional wave. While there is volumetric strain, there
is not average grain rotation.]
The measured ratio of compressional and shear wave speeds in granular media are known to be
inconsistent with elastic wave theory, which should be called "pseudo-elastic", since it is an application
of elastic wave equations to granular media, whose behavior is often different than that of an elastic
solid. The granular medium model developed here solves this inconsistency. As shown in Fig. 2, it is
consistent with a large proportion of the published data. The discrepancy with the remaining
measurements may be put down to residual moisture, which tends to lubricate the grain contacts,
causing slippage. The remaining data points fall between the granular medium and the lubricated grains
models (S=0).
t

Fig. 2. Comparison of measured and predicted shear-to-compressional squared speed ratios as a
function of confinement pressure.
[The plot shows the squared ratio of shear to compressional wave speeds as a function of
confinement pressure, from atmospheric pressure to 50 MPa. There are 3 horizontal lines
representing the pseudo-elastic, the granular, and lubricated granular medium models. A number of
data points, from measurements by Domenico, Bachrach et al., Prasad and Meissner, and Velea et
al., are clustered about the granular medium model. The remainder are between this and the
lubricated grain model. None are close to the pseudo-elastic model.]

(2) A new model of sediment reflection: The key parameters are the amplitude of the fluctuations and
the spatial correlation function of the sediment properties. Measurements of the bathymetry of the
SAX04 site by Kraft and de Moustier show that the spatial statistics can be dramatically altered by the
passage of a hurricane. Their measurements of bathymetry using multibeam sonars show significant
changes in the length scales of the bathymetric variations, from over 10 meters two weeks before the
hurricane, to less than 4 meters five weeks after. These values were estimated from the wavenumber
spectra of the interface roughness shown in Fig. 14 of Kraft and de Moustier 2010. These findings
show that the spatial statistics change significantly with time and weather events.

(3) Coupling of BIC08 to rough surface scattering models: A reduced-mesh model of an elastic
medium, with similar properties to water-saturated sand, was tested using OASES. The approach was
to replace the elastic medium half-space with a thin elastic layer overlaid on a fluid half-space of the
same density and compressional wave speed. To illustrate the problem, the reflection at the water-
elastic medium interface was computed at 5 kHz. The reflection loss curves are compared in the right
hand panel of Fig. 3. Two layer thicknesses were tried: at 0.06 m, the one-way shear wave attenuation
at the bottom of the layer would be 5 dB, and at 0.25 m, 20 dB. The reflection loss curves appear to be
indistinguishable. The difference between the half-space model and the layered models are shown in
the right panel. The differences are less than 0.06 dB. The region between 0 and the critical angle at 30
degrees is important for shallow water propagation computations. In this region, the 0.06 m layer had
differences of up to 0.003 dB, while the thicker layer gave differences less than ten times smaller.
Beyond the critical angle, the differences were larger and showed little correlation with layer thickness,
because they are caused by reflection of the compressional wave at the interface between the elastic
layer and the fluid half-space. Even though the density and compressional speeds are identical, the
difference in shear wave speed causes some reflection of the compressional wave at non-normal angles.

Fig. 3. Comparison of reflection magnitudes at the water-elastic medium interface for an elastic
half-space and for composites of an elastic layer over a fluid half space (left) and the differences
between the layered models and the elastic half-space (right).
[The left panel shows reflection magnitude in decibels plotted against the grazing angle, for an
elastic half-space and elastic layers overlaid on a fluid half-space. The rigth panel shows the
difference in dB between the elastic half-space model and the layered models. ]

IMPACT/APPLICATIONS

The results will impact Navy underwater acoustic propagation models, particularly where reflection
and penetration of sound at the ocean bottom are concerned. It will also impact the future structure of
oceanographic databases maintained by Navy offices, including the Naval Oceanographic Office.
Predictions of sediment wave speeds and attenuations will need to be revised.

TRANSITIONS

Work on s ediment variability is being transitioned to the active sonar trainers via the High-Fidelity
Active Sonar Training (HiFAST) project. Some aspects of the ocean sediment model, particularly the
frequency dependence of sediment attenuation, are being used in the Ocean Bottom Characterization
Initiative (OBCI) project.

RELATED PROJECTS

This project is closely related to most projects under the ONR Underwater Acoustics: High Frequency
Sediment Acoustics and Shallow Water Thrusts.

REFERENCES
N. P. Chotiros and M. J. Isakson, "A broadband model of sandy ocean sediments: Biot-Stoll with
contact squirt flow and shear drag," J. Acoust. Soc. Am., vol. 116, pp. 2011-2022, (2004).

N. P. Chotiros and M. J. Isakson, "High-frequency dispersion from viscous drag at the grain-grain
contact in water-saturated sand," J. Acoust. Soc. Am., vol. 124, pp. EL296-301, (2008).

N. P. Chotiros and M. J. Isakson, "Acoustic virtual mass of granular media," J. Acoust. Soc. Am.,
vol. 121, pp. EL70-EL76, (2007).

M. P. Goertz, J. E. Houston, and X.-Y. Zhu, "Hydrophilicity and the Viscosity of Interfacial
Water," Langmuir, vol. 23, pp. 5491-5497, (2007).

B. J. Kraft and C. P. de Moustier, "Detailed Bathymetric Surveys Offshore Santa Rosa Island, FL:
Before and After Hurricane Ivan (September 16, 2004)," IEEE J. Oceanic Eng., vol. 35, pp. 453-
470, (2010).

A. P. Lyons and D. A. Abraham, "Statistical characterization of high-frequency shallow-water
seafloor backscatter," J. Acoust. Soc. Am., vol. 106, pp. 1307-1315, (1999).

PUBLICATIONS

N. P. Chotiros, and M. J. Isakson. "Shear and compressional wave speeds in Hertzian granular
media," J. Acoust. Soc. Am., submitted 30 June 2010. [submitted, refereed]

K. R. Loeffler, and N. P. Chotiros. "The Calibration of a Laser Profiling System for Seafloor
Micro-topography Measurements," Optical Engineering Journal, submitted 27 August 2010.
[submitted, refereed]

M. J. Isakson, N. P. Chotiros, H. J. Camin, and J. Piper, "Bottom Loss Measurements in a Spatially
Variable Environment at the Sediment Acoustics Experiment 2004," J. Acoust. Soc. Am., submitted
2010. [submitted, refereed]

N. P. Chotiros, and M. J. Isakson. "Comments on "On pore fluid viscosity and the wave properties
of saturated granular materials including marine sediments" [J. Acoust. Soc. Am. 122, 1486-1501
(2007)]," J. Acoust. Soc. Am. 127, 2095-2098, (2010). [published, refereed]

N. P. Chotiros. "Non-Rayleigh distributions in underwater acoustic reverberation in a patchy
environment," IEEE J. Oceanic Eng. 35, 236-241, (2010). [published, refereed]

M. J. Isakson, and N. P. Chotiros. "Finite Element Modeling of a Shallow Water Waveguide,"
Proc. 10th European Conference on Underwater Acoustics, 5-9 July 2010, Istanbul, Turkey,
(2010). [published]

M. J. Isakson, and N. P. Chotiros. "Acoustic Scattering from a Poro-Elastic Sediment," Proc. 10th
European Conference on Underwater Acoustics, 5-9 July 2010, Istanbul, Turkey, (2010).
[published]
M. J. Isakson, and N. P. Chotiros. "A Finite Element Model of Propagation on the Southern and
Western Australian Continental Shelf," Oceans 2010, 24-27 May 2010, Sydney, Australia, 10110-
10001, (2010). [published]

N. P. Chotiros, and M. J. Isakson. "Shear waves in granular media," Proc. 10th European
Conference on Underwater Acoustics, 5-9 July 2010, Istanbul, Turkey, (2010). [published]

N. P. Chotiros, and M. J. Isakson. "Calcarenite as a poroelastic granular medium," Oceans 2010,
24-27 May 2010, Sydney, Australia, 100112-100009, (2010). [published]

N. P. Chotiros. "Shear speed anomaly in granular media," Engineering Mechanics Institute
Conference, 8-11 August 2010, Los Angeles, USA, (2010). [published]

N. P. Chotiros. "Classification of non-Gaussian reverberation as a mixture," J. Acoust. Soc. Am.
127, 2025, (2010). [published, invited]

M. J. Isakson, and N. P. Chotiros. "The effect of microbathymetry measurement resolution on
reverberation modeling," Proc. Pacific Rim Underwater Acoustics Conference, Xi'an, China, 23-25
September 2009, 3-6, (2009). [published]

M. J. Isakson, and N. P. Chotiros. "The effects of scattering and poro-elasticity in reflection
coefficient measurements," J. Acoust. Soc. Am. 126, 2168, (2009). [published]

N. P. Chotiros, and M. J. Isakson. "Wave propagation in water-saturated sand and grain contact
physics," Proc. Shallow Water Acoustics Conference, Shanghai, China, 16-20 September, 2009,
(2009). [published, invited]

N. P. Chotiros, and M. J. Isakson. "High-frequency dispersion from viscous drag at the grain-grain
contact in water-saturated sand," Proc. Pacific Rim Underwater Acoustics Conference, Xi'an,
China, 23-25 September 2009, 1-2, (2009). [published]

N. P. Chotiros, and M. J. Isakson. "Shear waves and grain-rolling in granular media," J. Acoust.
Soc. Am. 126, 2234, (2009). [published]